\documentclass[twoside]{article}
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\setlength{\textwidth}{6.7 in}
\setlength{\textheight}{8.5 in}
\setlength{\headsep}{0.75 in}
\setlength{\parindent}{0 in}
\setlength{\parskip}{0.1 in}
\usepackage{amsmath,amssymb,enumerate,algorithms,ifthen}

%
% The following commands sets up the lecnum (lecture number)
% counter and make various numbering schemes work relative
% to the lecture number.
%
\newcounter{lecnum}
\renewcommand{\thepage}{\thelecnum-\arabic{page}}
\renewcommand{\thesection}{\thelecnum.\arabic{section}}
\renewcommand{\theequation}{\thelecnum.\arabic{equation}}
\renewcommand{\thefigure}{\thelecnum.\arabic{figure}}
\renewcommand{\thetable}{\thelecnum.\arabic{table}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\NP}{\text{\rm NP}}
\newcommand{\DTIME}{\text{\rm DTIME}}
\newcommand{\polylog}{\text{\rm polylog}}
%
% The following macro is used to generate the header.
%
\newcommand{\lecture}[4]{
   \pagestyle{myheadings}
   \thispagestyle{plain}
   \newpage
   \setcounter{lecnum}{#1}
   \setcounter{page}{1}
   \noindent
   \begin{center}
   \framebox{
      \vbox{\vspace{2mm}
    \hbox to 6.28in { {\bf CMPUT 675: Topics on Approximation Algorithms and Approximability
                        \hfill Fall 2007} }
       \vspace{4mm}
       \hbox to 6.28in { {\Large \hfill Lecture #1: #2  \hfill} }
       \vspace{2mm}
       \hbox to 6.28in { {\it Lecturer: #3 \hfill Scribe: #4} }
      \vspace{2mm}}
   }
   \end{center}
   \markboth{Lecture #1: #2}{Lecture #1: #2}
   \vspace*{4mm}
}

%
% Convention for citations is authors' initials followed by the year.
% For example, to cite a paper by Leighton and Maggs you would type
% \cite{LM89}, and to cite a paper by Strassen you would type \cite{S69}.
% (To avoid bibliography problems, for now we redefine the \cite command.)
%
\renewcommand{\cite}[1]{[#1]}

\input{epsf}

%Use this command for a figure; it puts a figure in wherever you want it.
%usage: \fig{NUMBER}{FIGURE-SIZE}{CAPTION}{FILENAME}
\newcommand{\fig}[4]{
			\vspace{0.2 in}
			\setlength{\epsfxsize}{#2}
			\centerline{\epsfbox{#4}}
			\begin{center}
			Figure \thelecnum.#1:~#3
			\end{center}
	}

% Use these for theorems, lemmas, proofs, etc.
\newtheorem{theorem}{Theorem}[lecnum]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{definition}[theorem]{Definition}
\newenvironment{proof}{{\bf Proof:}}{\hfill\rule{2mm}{2mm}}

% Some useful equation alignment commands, borrowed from TeX
\makeatletter
\def\eqalign#1{\,\vcenter{\openup\jot\m@th
  \ialign{\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$\hfil
      \crcr#1\crcr}}\,}
\def\eqalignno#1{\displ@y \tabskip\@centering
  \halign to\displaywidth{\hfil$\displaystyle{##}$\tabskip\z@skip
    &$\displaystyle{{}##}$\hfil\tabskip\@centering
    &\llap{$##$}\tabskip\z@skip\crcr
    #1\crcr}}
\def\leqalignno#1{\displ@y \tabskip\@centering
  \halign to\displaywidth{\hfil$\displaystyle{##}$\tabskip\z@skip
    &$\displaystyle{{}##}$\hfil\tabskip\@centering
    &\kern-\displaywidth\rlap{$##$}\tabskip\displaywidth\crcr
    #1\crcr}}
\makeatother

% **** IF YOU WANT TO DEFINE ADDITIONAL MACROS FOR YOURSELF, PUT THEM HERE:


\begin{document}
%FILL IN THE RIGHT INFO.
%\lecture{**LECTURE-NUMBER**}{**DATE**}{**LECTURER**}{**SCRIBE**}
\lecture{1 Topic}{Date }{Mohammad R. Salavatipour}{Your Name}

% **** YOUR NOTES GO HERE:

% Some general latex examples and examples making use of the
% macros follow.  
%**** IN GENERAL, BE BRIEF. LONG SCRIBE NOTES, NO MATTER HOW WELL WRITTEN,
%**** ARE NEVER READ BY ANYBODY.
%This lecture's notes illustrate some uses of
%various \LaTeX\ macros.  
%Take a look at this and imitate.
%
%\section{Some theorems and stuff} % Don't be this informal in your notes!
%
%We now delve right into the proof.
%
%\begin{lemma}
%This is the first lemma of the lecture.
%\end{lemma}
%
%\begin{proof}
%The proof is by induction on \ldots.
%For fun, we throw in a figure.
%%%%NOTE USAGE !
%\fig{1}{1in}{A Fun Figure}{funfig.eps}
%
%This is the end of the proof, which is marked with a little box.
%\end{proof}
%
%\subsection{A few items of note}
%
%Here is an itemized list:
%\begin{itemize}
%\item this is the first item;
%\item this is the second item.
%\end{itemize}
%
%Here is an enumerated list:
%\begin{enumerate}
%\item this is the first item;
%\item this is the second item.
%\end{enumerate}
%
%Here is an exercise:
%
%{\bf Exercise:}  Show that ${\rm P}\ne{\rm NP}$.
%
%Here is how to define things in the proper mathematical style.
%Let $f_k$ be the $AND-OR$ function, defined by
%
%\[ f_k(x_1, x_2, \ldots, x_{2^k}) = \left\{ \begin{array}{ll}
%
%	x_1 & \mbox{if $k = 0$;} \\
%
%	AND(f_{k-1}(x_1, \ldots, x_{2^{k-1}}),
%	   f_{k-1}(x_{2^{k-1} + 1}, \ldots, x_{2^k}))
%	 & \mbox{if $k$ is even;} \\
%
%	OR(f_{k-1}(x_1, \ldots, x_{2^{k-1}}),
%	   f_{k-1}(x_{2^{k-1} + 1}, \ldots, x_{2^k}))	
%	& \mbox{otherwise.} 
%	\end{array}
%	\right. \]
%
%\begin{theorem}
%This is the first theorem.
%\end{theorem}
%
%\begin{proof}
%This is the proof of the first theorem. We show how to write pseudo-code now.
%%*** USE PSEUDO-CODE ONLY IF IT IS CLEARER THAN AN ENGLISH DESCRIPTION
%
%Consider a comparison between $x$ and~$y$:
%\begin{tabbing}
%\hspace*{.25in} \= \hspace*{.25in} \= \hspace*{.25in} \= \hspace*{.25in} \= \hspace*{.25in} \=\kill
%\>{\bf if} $x$ or $y$ or both are in $S$ {\bf then } \\
%\>\> answer accordingly \\
%\>{\bf else} \\
%\>\>    Make the element with the larger score (say $x$) win the comparison \\
%\>\> {\bf if} $F(x) + F(y) < \frac{n}{t-1}$ {\bf then} \\%
%\>\>\> $F(x) \leftarrow F(x) + F(y)$ \\
%\>\>\> $F(y) \leftarrow 0$ \\
%\>\> {\bf else}  \\
%\>\>\> $S \leftarrow S \cup \{ x \} $ \\
%\>\>\> $r \leftarrow r+1$ \\
%\>\> {\bf endif} \\
%\>{\bf endif} 
%\end{tabbing}
%
%This concludes the proof.
%\end{proof}
%
%
%\section{Next topic}
%
%Here is a citation, just for fun \cite{CW87}.
%

% **** THIS ENDS THE EXAMPLES. DON'T DELETE THE FOLLOWING LINE:

\section{This is the first section of the lecture}

% If you need to add references, use the following format:

%\section*{References}
%
%\begin{itemize}
%\item[CW87] {\sc D.~Coppersmith} and {\sc S.~Winograd}, 
%Matrix multiplication via arithmetic progressions,
%{\it Proceedings of the 19th ACM Symposium on Theory of Computing},
%1987, pp.~1--6.
%
%\item[S69] {\sc V.~Strassen}, Gaussian Elimination Is Not Optimal,
%{\it Numerische Mathematik\/~\bf13}, 1969, pp.~354--356.
%
%\item[P84] {\sc V.~Pan}, {\it How To Multiply Matrices Faster},
%Springer-Verlag, Lecture Notes in Computer Science Vol.~179, 1984.
%
%\end{itemize}

\end{document}


